mathsRus
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QUESTION 5
(i) Explain the difference between a type I error and a type II error.

Easy.

(ii) X is a Poisson random variable with unknown mean µ. A test is required of H0 : µ = 2
against H1 : µ > 2 based on the single value of X. A test which is suggested is to reject
H0 if the observed value of X is greater than 4.
(a) Calculate the probability of a type I error.

Answer: 0.90978

(b) Calculate the probability of a type II error if in fact µ = 5.

Answer: 0.175

(iii) X1, X2, . . ., X20 is a sequence of independent Poisson random variables, each having unknown mean µ. Suggest a test at the 5% level of significance of H0 : µ = 2 against H1 : µ > 2 based on this sample of size 20. You should answer by writing down the test statistic, the (approximate) distribution of the test statistic if the null hypothesis
is true and the critical region for this test.

Now for this one, I don't know which distribution to use. I thought of using t - test

Thanks for your time
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mathsRus
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Normally someone answer within minutes. If any problem, please tell.
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Kevin De Bruyne
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(Original post by mathsRus)
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For the last part I'm not sure what they want, though it could be a t test for one set of data.

If you wanted your answers checked for the previous questions you could post your working, or I could try to remember what type 1/2 errors are . So let me know if they need checking .
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cvbn
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I could be wrong as I don't do S2 or S3 or what3ver but if mu=2 then P(X>4)=0.0524 To get a typr 1 error you have to reject H0 when its true the probability of this is 0.0524 if mu=5 and you get a type 2 error if X<=4 then P(X<=4)=0.4405
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